LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zlaqhp ( character UPLO, integer N, complex*16, dimension( * ) AP, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, character EQUED )

ZLAQHP scales a Hermitian matrix stored in packed form.

Purpose:
``` ZLAQHP equilibrates a Hermitian matrix A using the scaling factors
in the vector S.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] AP ``` AP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A.``` [in] S ``` S is DOUBLE PRECISION array, dimension (N) The scale factors for A.``` [in] SCOND ``` SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i).``` [in] AMAX ``` AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.``` [out] EQUED ``` EQUED is CHARACTER*1 Specifies whether or not equilibration was done. = 'N': No equilibration. = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).```
Internal Parameters:
```  THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors.  If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.```
Date
September 2012

Definition at line 128 of file zlaqhp.f.

128 *
129 * -- LAPACK auxiliary routine (version 3.4.2) --
130 * -- LAPACK is a software package provided by Univ. of Tennessee, --
131 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132 * September 2012
133 *
134 * .. Scalar Arguments ..
135  CHARACTER equed, uplo
136  INTEGER n
137  DOUBLE PRECISION amax, scond
138 * ..
139 * .. Array Arguments ..
140  DOUBLE PRECISION s( * )
141  COMPLEX*16 ap( * )
142 * ..
143 *
144 * =====================================================================
145 *
146 * .. Parameters ..
147  DOUBLE PRECISION one, thresh
148  parameter ( one = 1.0d+0, thresh = 0.1d+0 )
149 * ..
150 * .. Local Scalars ..
151  INTEGER i, j, jc
152  DOUBLE PRECISION cj, large, small
153 * ..
154 * .. External Functions ..
155  LOGICAL lsame
156  DOUBLE PRECISION dlamch
157  EXTERNAL lsame, dlamch
158 * ..
159 * .. Intrinsic Functions ..
160  INTRINSIC dble
161 * ..
162 * .. Executable Statements ..
163 *
164 * Quick return if possible
165 *
166  IF( n.LE.0 ) THEN
167  equed = 'N'
168  RETURN
169  END IF
170 *
171 * Initialize LARGE and SMALL.
172 *
173  small = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
174  large = one / small
175 *
176  IF( scond.GE.thresh .AND. amax.GE.small .AND. amax.LE.large ) THEN
177 *
178 * No equilibration
179 *
180  equed = 'N'
181  ELSE
182 *
183 * Replace A by diag(S) * A * diag(S).
184 *
185  IF( lsame( uplo, 'U' ) ) THEN
186 *
187 * Upper triangle of A is stored.
188 *
189  jc = 1
190  DO 20 j = 1, n
191  cj = s( j )
192  DO 10 i = 1, j - 1
193  ap( jc+i-1 ) = cj*s( i )*ap( jc+i-1 )
194  10 CONTINUE
195  ap( jc+j-1 ) = cj*cj*dble( ap( jc+j-1 ) )
196  jc = jc + j
197  20 CONTINUE
198  ELSE
199 *
200 * Lower triangle of A is stored.
201 *
202  jc = 1
203  DO 40 j = 1, n
204  cj = s( j )
205  ap( jc ) = cj*cj*dble( ap( jc ) )
206  DO 30 i = j + 1, n
207  ap( jc+i-j ) = cj*s( i )*ap( jc+i-j )
208  30 CONTINUE
209  jc = jc + n - j + 1
210  40 CONTINUE
211  END IF
212  equed = 'Y'
213  END IF
214 *
215  RETURN
216 *
217 * End of ZLAQHP
218 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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